Question

During a certain week, the mean price of gasoline in the New England region was $3.796 per gallon. A random sample of 32 gas stations is selected from this population. What is the probability that the mean price for the sample was between $3.781 and $3.811 that week? Assume s = $0.045.

Answer 1

Answer: the probability that the mean price for the sample was between $3.781 and $3.811 that week is 0.94122

Explanation:

Given that;

sample size n = 32

mean μ = $3.796

standard deviation σ = 0.045

P(3.781 < x" < 3.811) = ?

Standard Error S.E = σ/√n = 0.045/√32 = 0.007955

z value for 3.781, z = x-μ/S.E = (3.781-3.796)/0.007955 = -1.8856 ≈ -1.89

z value for 3.811, z = x-μ/S.E = (3.811-3.796)/0.007955 = 1.8856 ≈ 1.89

P(3.781 < x" < 3.811) = P( -1.89 < z < 1.89)

= P(z < 1.89) - P(z < -1.89)

from z-score table

⇒ 0.9706 - 0.02938

⇒ 0.94122

Therefore the probability that the mean price for the sample was between $3.781 and $3.811 that week is 0.94122